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Example: Evaluating the Function
To evaluate the linear function for specific algebraic expressions, substitute each expression for the independent variable and simplify using the order of operations:
- Evaluate : Replace with to get . Simplify to yield .
- Evaluate : Replace with the binomial using parentheses to get . Distribute the to obtain . Simplify by combining the constant terms to find .
- Evaluate : This expression requires finding the value of first and adding it to the expression for . Find . Then, substitute both parts into the sum to get . Simplify by combining the constant terms to find .
Notice that evaluating a sum, such as , is not necessarily equal to the sum of the evaluated function values, .
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Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
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Example: Evaluating the Function at
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Example: Computing and for and
You are training to use your company's new logistics pricing software. The system's manual states that to determine the total shipping cost for a specific bulk order, you must 'evaluate the pricing function for the given number of units, .' According to the mathematical definition of evaluating a function, what exact process must you perform to achieve this?
You are a fitness instructor using a function to calculate the recommended daily water intake (in ounces) based on a client's weight (in pounds). To find the recommendation for a client who weighs 150 pounds, you must evaluate the function for . Arrange the following steps in the correct order to perform this evaluation process according to the standard mathematical procedure.
Evaluating Utility Costs
You are training to use a new inventory forecasting tool. The system's technical manual uses specific terminology to describe how it calculates projected stock levels using mathematical formulas. To ensure you can follow the manual's instructions, match each of the following terms with its correct mathematical definition based on the process of evaluating a function.
You are a business analyst working with a company pricing model, represented by the function , where is the number of items manufactured. True or False: To 'evaluate the pricing function' for a specific number of items, the correct mathematical process is to set the entire function equal to zero and solve for the independent variable .
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An inventory manager uses the function to calculate the estimated shipping cost for units of a product. Due to a change in packaging, the base order size has increased by 2 units, requiring the manager to evaluate the new cost using the expression . Arrange the steps below in the correct chronological order to evaluate and simplify this expression.
An operations analyst uses the linear function to estimate the total production time (in hours) for batches of a product. If the analyst needs to evaluate the production time for a quantity of batches represented by the expression , which of the following is the correct simplified expression for ?
A retail analyst uses the linear function to predict inventory costs based on variable batch sizes. Match each specific evaluation the analyst might perform with its correct simplified algebraic result.
A production analyst uses the linear function to estimate the total operating cost for machine hours. True or False: For this specific function, the cost of an extended run represented by is equivalent to the sum of the original cost and the cost of a 2-hour run, .
Comparing Function Evaluations in Cost Projections